Subgroups — #16777964

Order 3328.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129995	C₂	1	2	yes	maximal
2	#13112752	C₂	1	1	yes	maximal, characteristic
3	#11718249	—	2	2	no	—
4	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₄×#6090	C₂²	1	1	yes	characteristic
6	C₈×#1055	C₄	1	1	yes	characteristic
7	C₂×C₁₃×C₁₆	C₈	1	1	yes	characteristic
8	C₂×C₁₃×C₁₆	C₈	1	1	yes	characteristic
9	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂×#6090	D₄	1	1	yes	characteristic
11	C₂×#6090	Q₈	1	1	yes	characteristic
12	C₄×#1055	—	2	1	no	—
13	#88036	—	4	2	no	—
14	#7456	—	13	1	no	maximal, Sylow
15	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
18	C₂×#1055	—	2	2	no	—
19	C₁₃×C₁₆	—	2	1	no	—
20	C₁₃×C₁₆	C₁₆	1	2	yes	—
21	#6090	—	2	1	no	—
22	#6090	SD₁₆	1	2	yes	—
23	#1422	—	13	2	no	—
24	#1311	—	13	1	no	—
25	C₂×C₄×C₁₃	—	2	1	no	—
26	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
27	C₈×C₁₃	#106	1	1	yes	characteristic
28	C₈×C₁₃	#108	1	1	yes	characteristic
29	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
30	C₈×C₁₃	M₃₂	1	1	yes	characteristic
31	#1055	—	4	2	no	—
32	M₆₄	—	26	2	no	—
33	C₄×C₁₆	—	13	1	no	—
34	C₄×C₁₆	#261	1	1	yes	characteristic
35	C₈²	—	13	1	no	—
36	C₂²×C₁₃	#364	1	1	yes	characteristic
37	C₄×C₁₃	—	2	2	no	—
38	C₄×C₁₃	#334	1	1	yes	characteristic
39	C₄×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
40	C₂×C₁₆	—	13	1	no	—
41	C₂×C₁₆	—	13	1	no	—
42	C₂×C₁₆	#1057	1	1	yes	characteristic
43	C₂×C₁₆	#1057	1	1	yes	characteristic
44	C₄×C₈	—	26	1	no	—
45	C₄×C₈	C₂×#261	1	1	yes	characteristic
46	C₃₂	—	52	2	no	—
47	C₂×C₁₃	—	2	1	no	—
48	C₂×C₁₃	#1367	1	1	yes	characteristic
49	C₂×C₈	—	26	2	no	—
50	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
51	C₂×C₈	C₂×#1057	1	1	yes	characteristic
52	C₄²	#6118	1	1	yes	characteristic
53	C₁₆	—	2	1	no	—
54	C₁₆	—	13	2	no	—
55	C₁₆	—	26	1	no	—
56	C₁₆	#6092	1	2	yes	—
57	C₁₃	#7456	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₄⋊#1057	1	1	yes	characteristic
60	C₈	—	52	2	no	—
61	C₈	#88101	1	1	yes	characteristic
62	C₈	#88103	1	1	yes	characteristic
63	C₈	C₂×#6092	1	1	yes	characteristic
64	C₈	#88106	1	1	yes	characteristic
65	C₂²	#11718261	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	C₄⋊#6092	1	1	yes	characteristic
68	C₄	#11718253	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	#13129858	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#88101
commutator	C₈×C₁₃	C₂×C₁₆
Frattini	C₄×C₈	C₂×#261
Fitting	C₄×C₁₃×C₁₆	C₄
socle	C₂×C₁₃	#1367
prime radical	C₂²×C₁₃	#364
cosocle	C₄×#6090	C₂²
hypercenter	C₄×C₁₆	#261
hypocenter	C₁₃	#7456
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
57. C₁₃	#7456	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13129995	2
#13112752	2
#7456	13